Second-order performance analysis of standard ESPRIT

This paper provides a second-order (SO) analytical performance analysis of the 1-D Standard ESPRIT algorithm. Existing performance analysis frameworks are based on first-order (FO) approximations of the parameter estimation error, which are asymptotic in the effective signal-to-noise ratio (SNR), i.e., they become exact for either high SNRs or a large sample size. However, these FO expressions do not capture the algorithmic behavior in the threshold region at low SNRs or for a small sample size. Yet, such conditions are often encountered in practice. Therefore, we present a closed-form expression for the parameter estimation error of 1-D Standard ESPRIT up to the SO that is valid in a wider effective SNR range. Moreover, we derive an analytical mean square error (MSE) expression, where we assume a zero-mean circularly symmetric complex Gaussian noise distribution. Finally, we use the existing FO MSE expression and the derived SO MSE expression to analytically compute the SNR breakdown threshold of the MSE threshold region. Empirical simulations verify the analytical expressions.